1. Dot plots show how data is distributed (spread out)
using a number line.

2. What can you say or work out from this data?
Example : A group of students measure their pulse
rates when resting. The rates are
66, 69, 62, 58, 74, 56, 67, 72, 61, 62, 59
What can you say or work out from this data?
1. Lowest value is 56 BPM
2. Highest value is 74 BPM
3. Mode is 62 BPM
4. Median is also 62 BPM
5. Distribution is flat 50 60 70 80

3. Common expressions for various dot plots.
By looking at the shape of the distribution try to describe the six possible types.
Common expressions for various dot plots.
Symmetrical distribution
Wide spread distribution
Uniform distribution
Tightly clustered distribution
Skewed right distribution
Skewed left distribution

4. Five Figure Summary When a set of numbers are put in ORDER,
it can be summarised by quoting five figures.
1. The highest number (H)
2. The lowest number (L)
3. The median, the number that halves the list (Q2)
4. The upper quartile, the median of the upper half (Q3)
5. The lower quartile, the median of the lower half (Q1)

5. Q2 = Median (middle value)
Five Figure Summary
Q2 = Median (middle value)
Q1 = lower middle value
Example Find the five figure summary for the data.
2, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10
Q3 = upper middle value
The 11 numbers are already in order !
Q1 = 5
Q2 = 7
Q3 = 8 2 4 5 6 7 7 8 9 10
L = 2
H = 10

6. Five Figure Summary Example Find the five figure summary for the data.
Q2 = Median (middle value)
Example Find the five figure summary for the data.
2, 4, 5, 5, 6, 7, 7, 8, 9, 10
Q1 = lower middle value
Q3 = upper middle value
The 10 numbers are already in order !
Q1 = 5
Q2 =
6·5
Q3 = 8 2 4 5 6 7 8 9 10
L = 2
H = 10

7. Five Figure Summary Example Find the five figure summary for the data.
2, 4, 5, 5, 6, 7, 8, 9, 10
Q2 = Median (middle value)
Q1 = lower middle value
Q3 = upper middle value
The 9 numbers are already in order !
Q1 =
4·5
Q2 = 6
Q3 =
8·5 2 4 5 6 7 8 9 10
L = 2
H = 10

8. Two middle values so take the mean.
Averages (The Median)
The median is the middle value of a set of data once the data has been ordered.
Example 1. Tim hit 12 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives.
85, 125, 130, 65, 100, 70, 75, 50, 140, 135, 95, 70
50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 135, 140
Two middle values so take the mean.
Order the data
Median drive = 90 yards

9. Inter- Quartile Range = 9 - 5½ = 3½
Finding the median, quartiles and inter-quartile range.
Example 1: Find the median and quartiles for the data below.
12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10
Order the data
Median = 8 Q2
Lower Quartile = 5½ Q1
Upper Quartile = 9 Q3
4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12
Inter- Quartile Range = 9 - 5½ = 3½

10. Inter- Quartile Range = 10 - 4 = 6
Finding the median, quartiles and inter-quartile range.
Example 2: Find the median and quartiles for the data below.
6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10
Order the data
Lower Quartile = 4 Q1
Median = 8 Q2
Upper Quartile = 10 Q3
3, 4, 4, 6, 8, 8, 8, 9, , 10, 15
Inter- Quartile Range = = 6

11. Anatomy of a Box and Whisker Diagram.
Box and Whisker Diagrams.
Box plots are useful for comparing two or more sets of data like that shown below for heights of boys and girls in a class.
Anatomy of a Box and Whisker Diagram.
Lower Quartile
Upper Quartile
Lowest Value
Highest Value
Median
Whisker
Box 4 5 6 7 8 9 10 11 12
130
140
150
160
170
180
190
Boys
Girls

12. 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12
Example 1: Draw a Box plot for the data below
Drawing a Box Plot.
Median = 8 Q2
Lower Quartile = 5½ Q1
Upper Quartile = 9 Q3 4 5 6 7 8 9 10 11 12

13. Drawing a Box Plot.
Example 2: Draw a Box plot for the data below
Lower Quartile = 4 Q1
Median = 8 Q2
Upper Quartile = 10 Q3
3, 4, 4, 6, 8, 8, 8, 9, , 10, 15, 3 4 5 6 7 8 9 10 11 12 13 14 15

14. Drawing a Box Plot.
Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data.
Median = 171 Q2
Lower Quartile = 158 Q1
Upper Quartile = 180 Q3
137, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186
130
140
150
160
170
180
190

15. Drawing a Box Plot
Question: Gemma recorded the heights in cm of girls in the same class and constructed a box plot from the data. The box plots for both boys and girls are shown below. Use the box plots to choose some correct statements comparing heights of boys and girls in the class. Justify your answers.
130
140
150
160
170
180
190
Boys
Girls
1. The girls are taller on average.
2. The boys are taller on average.
3. The girls show less variability in height.
5. The smallest person is a girl
4. The boys show less variability in height.
6. The tallest person is a boy